Exo1: Let the series $$ \sum h_{n} $$ such as, $$ \forall n \in \mathbb{N}, \forall x \in \mathbb{R}_{+} ; h_{n}(x)=(-1)^{n} \frac{n}{n^{2}+x}: $$ 1. Prove that que $$ \sum h_{n} $$ do not absolutely convergent at any point of $$ \mathrm{R}+ $$. 2. Prove that que $$ \sum h_{n} $$ converges uniformly on $$ \mathrm{R}+ $$ Voir: $$ \underline{ ext { Asanalyse 1-2-3 Guelma.pdf }} $$ exo1 page 372

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Exo1: Let the series $$ \sum h_{n} $$ such as, $$ \forall n \in \mathbb{N}, \forall x \in \mathbb{R}_{+} ; h_{n}(x)=(-1)^{n} \frac{n}{n^{2}+x}: $$ 1. Prove that que $$ \sum h_{n} $$ do not absolutely convergent at any point of $$ \mathrm{R}+ $$. 2. Prove that que $$ \sum h_{n} $$ converges uniformly on $$ \mathrm{R}+ $$ Voir: $$ \underline{	ext { Asanalyse 1-2-3 Guelma.pdf }} $$ exo1 page 372

Barnett Logan · Accepted Answer

The series $$ \sum h_{n} $$ does not absolutely converge at any point of $$ \mathbb{R}_{+} $$ and converges uniformly on $$ \mathbb{R}_{+} $$.

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